Geometry Big Ideas
• inductive reasoning - specific events are used to
make generalizations (Reasoning based on Patterns)
ex. It rained Monday, 10-11, and on Monday 10-, and
on Monday 9-27. So, the generalization or Pattern
is that it rains on Mondays.
Another example:
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3x180 =540
3x180 =720
• deductive reasoning ­ generalizations are used to arrive at a specific conclusion.......reasoning based on the laws of logic, facts, definitions, and/or accepted properties
• conjecture ­ an unproven statement based on observations
• conditional statement ­ an "if­then" statement with a hypothesis and a conclusion
* if hypothesis, then conclusion
* if p, then q
* p -> q (read " p implies q")
• converse statement
* if conclusion, then hypothesis
* if q, then p
* q -> p (read " q implies p"
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• inverse statement
* if not hypothesis, then not conclusion
* if not p, then not q
* ~p -> ~q (read "not p implies, not q")
• contrapositive statement
* if not conclusion, the not hypothesis
* if not q, then not p
* ~q -> ~p (read "not q implies not p")
• EQUIVALENT STATEMENTS - A conditional statement and
its contrapositive are both true or they are both false.
A converse statement and its inverse statement are both true
or they are both false.
So, Conditional = Contrapositive
(in truth value)
and Converse = Inverse
(in truth value)
If 2 statements are both true or they are both false,
they are equivalent statements.
Example of EQUIVALENT STATEMENTS
conditional
converse
inverse
contrapositive
conditional
converse
inverse
contrapositive
• Given the statement: ants are insects
Underline the hypothesis once and the conclusion twice,
then write the conditional, converse, inverse, and
contrapositive.
ants are insects
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Conditional: If it is an ant, then it is an insect.
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Converse: If it is an insect, then it is an ant.
F
Inverse: If it is not an ant, then it is not an insect.
Contrapositive: If it is not an insect, then it is not an ant. T
The conditional and the contrapositive statements are both
true and are EQUIVALENT STATEMENTS. The converse
and the inverse statements are both false and are
EQUIVALENT statements.
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